Quantization of massless fields over the static Robertson-Walker space of constant negative curvature (Q2752502)

The construction of a quantum field theory in a curved space is an important problem of mathematical physics [\textit{N. D. Birrell} and \textit{P. C. W. Davies}, Quantum fields in curved space. Cambridge University Press, Cambridge (1982; Zbl 0476.53017) and Corr. reprint (1984; Zbl 0972.81605)]. The purpose of the present paper is to review the application of the method of coherent states to the quantization of massive spin-0 and spin-\({1 \over 2}\) fields on the de Sitter space [\textit{D.-E. Liebscher}, Einsteins Relativitätstheorie und die Geometrien der Ebene. Teubner, Stuttgart, Leipzig (1999)], and the application of the technique of plane wave quantization to massive spin-0 fields on Robertson-Walker spaces [\textit{S. W. Hawking} and \textit{G. F. R. Ellis}, The large scale structure of space-time. Cambridge University Press, Cambridge (1973; Zbl 0265.53054), reprint 1999]. In addition, the paper presents an extension of the earlier results to the quantization of massless fields of arbitrary non-zero spin on Robertson-Walker spaces [\textit{E. Binz, S. Pods}, and \textit{W. Schempp}, Spinor geometry and signal transmission in three-space. Proceedings CASYS 2001, Liège 2002 (in press); Space-time geometry and quantum information transmission: encoding and detection. Manuscript (to appear)].